If I had to venture a guess, I would say the glazed zisha teapot is early Republican Period. I have a couple and the colors and design of the glaze is similar to pieces I have from that period. It was also very common, at this time to use the names of famous potters on zisha products. A lot of porcelain pieces from the period are marked with the reign date of Emperor Tongzhi of the Qing Dynasty.

two little cups I just got, I do not really know anything about them. Looks like japanese, i'd guess meiji period. They are about 4.5 cm or 1 and 3/4 inches across. They're not Kutani, Imari, Satsuma. So, I don't know what to call them. Very delicate and beautiful though.

edit : the one with the writing inside looks like it could be kutani ware from the mark on the bottom.

Thanks for the replies. Here are pictures of the bottoms and side. The character on the right cup, look like the image 591 on this pagehttp://gotheborg.com/marks/kutani.shtml, but it is not red like most kutani ware.